Anti-windupSpeedControlofanACServoDrive.doc

2002中華民國自動控研討會

Anti-windup Speed Control of an AC Servo Drive
Ming-Shyan Wang*, Houang-Wen Laio**, Wang-Cheng Chen**, and Hong-Zgi Chen*
王明賢*,廖鴻文**,陳旺承**,陳鴻志*
*Department of Electronic Engineering, Southern Taiwan University of Technology
1,Nan-Tai St.Yung Kang City, Tainan Hsien, Taiwan, 710
TEL:[phone] ext.3125 E-mail:[e-mail]
** Eternity Electronics Industry Co., Ltd. TEL:[phone]

498

Abstract
In the paper, the anti-windup PI control is studied for the commercial AC servo motor drive. The self-conditioned algorithm is used. In the experimental test, control loop bandwidth, per-normal (PN) inertia, and noise sensitivity are considered. And the load shock recovery is also tested.
Keywords: Anti-windup PI control, AC servo motor drive, self-conditioned algorithm.
摘要
本文針對工業用AC伺服馬達驅動器之速度控制，以自我條件法則探討重置捲起的問題。實驗上，將速度迴路頻寬、單位正規慣量、雜訊靈敏度與負載干擾恢復時間等規格皆列入討論。
關鍵字:反重置捲起比例積分控制,交流伺服馬達驅動器,自我條件法則.
1. Introduction
It is well-known that the permanent-magnet synchronous motor (PMSM) has the advantages of higher torque-to-inertia ratio and power density when compared to the induction motor or the wound-rotor synchronous motor [1-4]. So, a PMSM is often used for the commercial AC servo drive. Then, the research and manufacture of AC servo drives become more popular and competitive. However, except for the most important specification performance, there are some realistic terms considered in the commercial AC servo drive, such as cost, complexity

of functions, and generality of used components, etc. Some guidelines are provided for interpretation of AC/DC drive speed performance specifications from a drive system’s application perspective in [5].
The windup problem in controllers is an adverse effect that occurs in the integral action of PID control, when nonlinearities exist between the controller output and the plant input [6-9]. It has been found that this phenomenon may be overcome by some anti-windup schemes, such as conventional anti-windup (CAW), Hanus conditioned controller, general conditioning technique (GCT), and observer-based anti-windup, and so forth.
In the paper, the HO series drives, designed under the cooperation between teachers and students with the department of electronic engineering of STUT and the manager Fu-Sun Hsu of EEI, for AC servo motors (PMSM type) of Sinano company are considered. The proportional-integral-anti-windup algorithm is tested in the velocity loop control. And the guidelines in [5] are used for HO drives.
This paper is organized as follows. Section 1 is the introduction. In section 2, the single phase model and the dq-transform model of HO drives are investigated. Section3 describes the windup problem in the control system, and the conditioned PI controller. In section 4, the experimental results are shown, and the analysis of the guidelines in [5] is given. Finally, some conclusions are made.
2. PMSM and its drive
2002中華民國自動控研討會

The model of a PMSM is given by [10,11]
(1)
where ,and ,, represent the phase-j voltage , current and back emf, respectively , and . The following linear transformation is used to obtain dq-axis representation [10,11]
(2a)
where is the electric angle between the stator and the rotor, and its inverse transformation is
(2b)
By using (2a), we have
(3)
where is armature resistance (inductance), and is the electric velocity. The electric torque of the motor is
(4)
where is the torque constant .
If the model (3) is used, we know that the control of (3) is easier than that of (1). The output torque of the motor is only determined by . And, it has higher efficiency on power for , and works magnetic field weakening for negative . However, it’s necessary to use the linear transformation (2a) and inverse transformation (2b) in the control loop. Although, the calculation of (2a) and (2b) can be replaced with lookup table. It would need a while time for a non-DSP type, general micro-controller, for example, 16-bit M16C/62 group. And the dq-model is not available for the brushless DC motor (BLDCM). So, for uniform design algorithm of drives of PMSM and BLDCM, the single phase model (1) is adopted in HO series drives even the necessary compensation for in the control loop.
Fig.1 shows that there are three closed-loops, current control, velocity control, and position control, in the servo control system. And, Fig.2 shows the block diagram of the drive hardware. The 16-bit M16C micro-controller provides sufficient ROM for program instructions, multifunctional 16-bit timers to generate 3-phase PWM signals, 25 internal and 8 external interrupt sources, serial I/O for RS232C and RS485, 10 bits * 8 channels ADC, 8 bits * 2 channels DAC, one watchdog timer, some programmable I/Os, and 62.5ns the shortest instruction execution time at fin=16MHz, etc. The I/O interface and encoder interface are designed in the CPLD. The intelligent power unit (IPM) is the main chip of the inverter of the drive. IPM provides some protections, such as over-current, overheat, load short-circuit, and under-voltage detections. There are three kinds of drives in HO series on their maximum collector currents, 15A, 20A, and 30A, respectively.
The PI control is applied to the velocity control loop of the drive to get the zero steady-state error. And, the proportional gain constant and integral gain constant are adjustable according to the load. However, the windup problem and load disturbance have to be considered in the adjust procedure.

3. Anti-windup design
In a linear control system, if there is an integral action in its controller and a limiter in the plant, it will integrate the error signal such that the integral term may become very large if integration lasts for a long time and saturation occurs. It is true because all physical systems are subject to actuator saturation or limitation. This is called windup problem.
However, the windup problem in the integrator part of the controller is only a special case of a general problem. The general windup problem is described in Fig 3. There exists a non-linearity between linear controller output and plant input [6-9] . And, the lack of consistency in the controller states may give rise to a deterioration of control performance.
Consider a linear and discrete controller [7],
(5a)
(5b)
where the matrices and have the appropriate dimensions , is invertible ,is controller state vector , is reference input vector , and is output vector . The corresponding unconditioned discrete-time controller shown in Fig.4 fulfills the equation:
(6)
where and are square matrices and given by
(7a)
(7b)
and q is the forward shift operator,
(8)
The self-conditioned controller shown in Fig.5 is given by [7].
vr(t+1)=[A(t)-B(t)D-1(t)C(t)]*vr(t)+B(t)D-1(t)ur(t)
+[B(t) D-1(t)F(t)-E(t)]*y(t)
u(t)=D(t){w(t)-T-1(q,t)*S(q,t)y(t)+[D-1(t)- T-1(q,t)]
*u(t)}
where state vector , obtained with auxiliary input to cancel the effects of the nonlinearities, are necessarily adequate .
2002中華民國自動控研討會

If a PI controller is considered, the conditioned structure is shown in Fig.6, and yields:
(9a)
(9b)

4. Experimental results
The experimental arrangement is 6CC401 PMSM whose parameters are shown in Table 1, driven by H15 drive with a 3.45 Kgcm2 dummy load. Fig.7 shows the 3000 rpm step responses for and torque limit with ant-windup control and without anti-windup control, respectively; and their corresponding waveforms of current command and. Fig.8 shows the results for and . Fig. 9 depicts the waveforms for and , and Fig.10 depicts the results for and . Replacing the dummy load with the other PMSM, the results are shown in Figs.11 and 12 for 4 cases: and (generator output current),and, , and , respectively.
From Figs.7-12, we know that the system controlled by anti-windup algorithm has better speed response of smaller overshoot, and needs less current to drive the motor, for lower proportional gain .For higher , the responses of two control systems are almost same. These situations also happen on load disturbance applied to system. However, the anti-windup control system has longer rise time.
Assuming the system natural frequency/loop bandwidth=10 and PN Noise=0.001, we have other parameters, torque loop bandwidth=4500 rad/s and speed sample time=0.2 ms. By [1], the procedure to find the maximum speed loop bandwidth is:
Step 1:
Step 2: (PN inertia),
Step 3: theoretical ,
Step 4: constrained ,
Step 5: final .
It is known that the performance of the speed loop was constrained by the drive technology. This constraint is caused by the current loop bandwidth, due to the non-specific DSP motor control chip, MC16, and the delay time of the power IC in the inverter. And, from Figs. 11 and 12, we find that the shock recovery time is very short.

5. Conclusions
The speed control is studied in the commercial AC servo motor drive. Self-conditioned PI control algorithm is researched for further discussion. It is shown that the response under self-conditioned PI control has the smaller overshoot and damping, but longer rise time. The specifications of control loop bandwidth, PN inertia, noise sensitivity, and load shock recovery time are discussed. However, the torque-speed response on self-conditioned PI control has not tested yet. Further, although the performance of speed loop bandwidth is constrained by torque loop bandwidth, HO drives still have about 900 rad/s speed loop bandwidth by using non-specific DSP motor control chip for other considerations.

Output power

400W
Torque

1.274 N．m
Stator Current

3.5A
Speed

3000 rpm
Torque Constant

0.409 Nm/A
back emf constant

42.8 V/Krpm
inertia

0.29 Kg．cm2
Stator Resistance

2.81
Stator inductance

6.33 mH
Table 1. Parameters of 6CC401 PMSM

2002中華民國自動控研討會

Fig.1 Block diagram of a drive
Fig.2 Hardware architecture of a drive
ur(t)
u(t)
Fig.3 Classical unconditioned control loop

Fig-4. Non-conditioned structure

Fig. 5 Self-conditioned structure
Fig.6 Self-conditioned PI controller

Fig. 7(a) anti-windup PI Fig. 7(b) PI control
The 3000rpm step responses for Kp=0.625 and TLMT=TR: speed command, response, iu, and current command.

Fig. 8(a) anti-windup PI Fig. 8(b) PI control
The 3000rpm step responses for Kp=4.375 and TLMT=TR: speed command, response, iu, and current command.

2002中華民國自動控研討會

Fig. 9(a) anti-windup PI Fig. 9(b) PI control
The 3000rpm step responses for Kp=0.625 and TLMT=3TR: speed command, response, iu, and current command.

Fig. 10(a) anti-windup PI Fig. 10(b) PI control
The 3000rpm step responses for Kp=4.375 and TLMT=3TR: speed command, response, iu, and current command

Fig. 11(a) Kp=0.625, Fig. 11(b) Kp=0.625, PI anti-windup control

Fig. 11(c) Kp=4.375, Fig. 11(d) Kp=4.375, PI anti-windup control
The speed loop load shock recovery tests for ig=2A and TLMT=TR: speed response, load shock

Fig. 12(a) Kp=0.625, Fig. 12(b) Kp=0.625, PI anti-windup control

Fig. 12(c) Kp=4.375, Fig. 12(d) Kp=4.375, PI anti-windup control
The speed loop load shock recovery tests for ig=5A and TLMT=3TR: speed response, load shock.

References
[1] P.Pillay and R.Krishnan , “ Modeling, Simulation,, and analysis of Permanent-Magnet Motor Drives, Part I : The Permanent-Magnet Synchronous Motor Drive “ , IEEE Trans. on Ind. Appl., vol. 25, No. 2, pp.265-273, 1989.
[2] P.Pillay and R.Krishnan, “ Modeling, Simulation, and analysis of Permanent-Magnet Motor Drives, Part II: The Permanent-Magnet Synchronous Motor Drive “, IEEE Trans. on Ind. Appl. , vol. 25 , No. 2 , pp.274-279 , 1989.
[3] J.P.Karunadasa and A.C. Renfrew, “ Design and implementation of microprocessor based on sliding mode controller for brushless servomotor “, IEE Proc-B, vol. 138, No. 6, pp.345-363, 1991.
[4] J.-L. Hsien , Y.-Y. Sun, and M.-C. Tsai, “ H∞ control for a sensorless permanent-magnet synchronous drive “ , IEE Proc-Electr. Power Appl., vol. 144 , No. 3 , pp.173-181 , 1997.
2002中華民國自動控研討會

[5] B.T. Boulter, “ Applying Drive Performance Specifications to Systems Applications—Part I : Speed Performance “ , IEEE Trans. on Ind. Apple., Vol.37 ,No. 4 ,pp.1082-1087 , 2001.
[6] A.H. Glattfelder and W. Schaufelberger, “ Stability Analysis of Single Loop Control Systems with Saturation and Antireset-windup Circuits “, IEEE Trans. Automat. Control, Vol. 28, No. 12, pp.1074-1081, 1983.
[7] R. Hanus, M. Kinnaert, and J.-L. Henrotte, “ Conditioning Technique, a General Anti-windup and Bumpless Transfer Method “ , Automatica, Vol. 23 , No.6 , pp.729-739 , 1987.
[8] K.S. Walgama, S. Ronnback, and J.Sternby, “ Generalisation of Conditioning technique for Anti-windup Compensators “, IEE Proc.-D, Vol. 139, No.12, pp.109-118, 1992.
[9] M.V. Kothare, P.J. Campo, M.Morari, and C.N. Nett, “ A Unified Framework for the study of Anti-windup Designs “, Automatica, Vol. 30, No. 12, pp.1869-1883, 1994.
[10] 劉昌煥主編,電機機械, 東華書局, 1999
[11] 王明賢, “全數位AC伺服馬達驅動器研製”,第一屆全國技專校院工程技術類產學合作暨技術移轉成果發表會,電機10-1,2001

Acknowledgments
The authors would like to express their appreciation to colleagues, Dr. Ten-Chuan Hsiao and Chao-Ming Huang with Southern Taiwan University of Technology, and Manager Fu-Sun Hsu with EEI, for their support on CPLD, software, and hardware. This work was also supported by NSC under contact NSC 90-2213-E-218-017.